(sin(57.22))/(31.5)=(sin(θ))/(24.4)

Lösung

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( θ )}{24.4}

θ = 0.70923 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

Radianten

θ = 0.70923 \dots + 2 πn, θ = π - 0.70923 \dots + 2 πn

Schritte zur Lösung

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( θ )}{24.4}

Tausche die Seiten

\frac{sin ( θ )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

Multipliziere beide Seiten mit

24.4

\frac{sin ( θ )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

Multipliziere beide Seiten mit

24.4

\frac{24.4 sin ( θ )}{24.4} = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

Vereinfache

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

Wende die Eigenschaften der Trigonometrie an

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

Allgemeine Lösung für

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

θ = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

θ = 0.70923 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

7.5 sin (x) = 3.4 cos (x)

sec (θ) = 8, tan (θ) = 37

tan (3 x - 4) = \frac{- 1}{2}

2 + 3 sec (x) - 4 cos (x) = 23

4 sin (x) \cdot cos (x) = 2 sin (x)